International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 2
Number 4
December 2008
359
Fuzzy Collision Threat Parameters Area
(FCTPA) – A New Display Proposal
R. Szlapczynski
Gdansk University of Technology, Gdansk, Poland
ABSTRACT: The paper introduces a visualization method that enables the navigator to estimate an encounter
situation and choose collision avoidance manoeuvre if necessary. It is based on the CTPA method and offers
new features: fuzzy sectors of forbidden speed and course values and the possibility to use any given ship
domain. The method is fast enough to be applied in the real-time decision-support system.
1 INTRODUCTION
Traditional displays used in collision-avoidance
systems were based on the relative Cartesian
coordinate system, with the own ship in the centre of
it and X and Y coordinates denoting the relative
positions of targets. Their functionality was limited
to showing all targets within a certain range and
indicating the targets that were considered to be
dangerous on the basis of computations performed
by the system. Some of them additionally visualized
Predicted Areas of Danger (PAD) and the resulting
necessary course alterations. What these displays
failed to visualize was the nature of collision risk:
the colliding combinations of courses and speeds of
the own ship and the dangerous targets. Visualizing
these forbidden combinations of course and speed
(instead of course only) has been introduced by
Lenart as a part of Collision Threat Parameters Area
(CTPA) method in (Lenart 1982). However, the
display according to Lenart naturally assumes using
a pre-defined safe distance DS as a main safety
parameter and DCPA as a collision risk measure.
Therefore it cannot be used for precise visualization
of the necessary manoeuvres when domains other
then circle-shaped are assumed. The author of the
paper has combined the following ideas: double
coordinate system used in CTPA, a fuzzy ship
domain (Pietrzykowski 2001) and approach factor
fmin – a new measure of collision risk defined by
the derived from the concept of a ship domain
(Szlapczynski 2006). Approach factor fmin is
defined as the scale factor of the largest domain-
shaped area that is predicted to remain free of other
ships throughout the whole encounter situation.
The result is a new visualization method called
Fuzzy Collision Threat Parameters Area (FCTPA). It
is based on Collision Threat Parameters Areas
method and extends it so as to handle any given
domain, including fuzzy domains. The rest of the
paper is organized as follows. Section 2 briefly
describes the CTPA method. In Section 3 the new
method of visualization – FCTPA is presented. In
Section 4 an example of planning the last chance
manoeuvre using the FCTPA method is provided.
Finally Section 5 is a summary of the paper.
2 COLLISION THREAT PARAMETERS AREAS
(CTPA)
In (Lenart 1982) a collision threat is defined as a
target ship for which the following condition holds:
S
DDCPA <
(1)
360
The method uses a double Cartesian coordinate
system where the horizontal axis represents both the
X coordinate of position and VX coordinate of speed
and the vertical axis represents both the Y coordinate
of position and VY coordinate of speed. The relation
between the position and speed coordinates is as
follows:
τ,*
τ,*
y
x
Vy
Vx
=
=
(2)
where τ is a fixed time value, for example 12
minutes.
The Collision Threat Area for a single target ship
is defined as an area in the abovementioned system
of coordinates that fulfils the following conditions:
− placing the tip of the own speed vector V within
this area would result in violating the safe
distance D
S
between the own ship and the target,
− placing the tip of the own speed vector V outside
this area would result in keeping the safe distance
D
S
between the own ship and the target.
− The Collision Threat Area for a group of target
ships is defined as a superposition of the
Collision Threat Areas obtained for each of the
targets separately.
The formula for the two straight lines determining
the boundaries of the CTPA for a given single target
is as follows:
τ
τ
22
11
bxay
bxay
−=
−=
(3)
where the coefficients are given by the formulas:
,
,
22
222
2
22
222
1
Sr
SrrSrr
Sr
SrrSrr
Dx
DyxDyx
a
Dx
DyxDyx
a
−
−+−
=
−
−++
=
(4)
,
,
22
11
tytx
tytx
VVab
VVab
−=
−=
(5)
where:
x
r
, y
r
– coordinates of the relative position of the
target ship,
V
tx
, V
ty
– coordinates of the true speed of the
target ship.
In practice CTPA is only this part of the
determined area, where the condition TCPA > 0
holds, since only future collision threats are of
interest. Also, in case of a multiple target encounter,
the manoeuvres for which the safe distance D
S
would be violated after a time longer than the critical
time (DCPA<D
S
, TCPA > T
S
) may be allowed, if
there is no possibility of avoiding all targets with just
one manoeuvre. This means that the tip of the own
speed vector may be conditionally placed within this
part of the CTPA, for which TCPA > T
S
.
When applied to the graphical display, the CTPA
method enables the operator to choose manually a
safe own speed vector in a very easy way – it is
enough to choose a point outside the CTPA and read
its speed coordinates. The method is summarized by
Figure 1.
Fig. 1. The Collision Threat Parameters Areas method
3 FUZZY COLLISION THREAT PARAMETERS
AREA
In this section a visualization tool that has been
designed by the author – Fuzzy Collision Threat
Parameters Area (FCTPA) is presented. It is based
on the same concept of the forbidden area in the
double Cartesian coordinate system, but instead of
determining the area analytically for a fixed DS
value, it is determined numerically for a given ship
domain. It works as follows. For every combination
of the own course and speed the resulting fmin value
is computed. The algorithms used to compute the
fmin value for given courses, positions and speeds of
the own ship and target ships have been presented in
detail in (Szlapczynski 2006). Depending on the
obtained value, a point in the double Cartesian
coordinate system representing a particular
combination of the own speed and course is assigned
a colour in the following way:
− for f
min
< 0.5 (critical domain violation): black,
361
− for 0.5 ≤ f
min
< 1 (domain violation): gradually
changing dark grey,
− for 1 ≤ f
min
< 2 (close encounter): gradually
changing light grey,
− for f
min
> 2 (safe passing): white.
Whenever the arrow indicating the end of the own
speed vector appears on the dark grey or black
background – a collision avoidance manoeuvre
should be performed. A safe combination of the own
speed and course is represented by the closest white
or light grey point on the display. An exemplary
situation is presented below. The data for the
scenario is given in Table 1. In Figures 2 – 6 the
relative positions, relative courses and relative
speeds of targets as well as the resulting FCTPA are
shown. The domain according to Coldwell
(Coldwell 1982) is used here.
Fig. 2. The FCTPA for the given scenario for the start time (t
=0 min.)
Fig. 3. The FCTPA for the given scenario for the time t = 5
min.
Fig. 4. The FCTPA for the start time of the given scenario for
the time t = 10 min.
Fig. 5. The FCTPA for the given scenario for the time t = 15
min.
Fig. 6. The FCTPA for the given scenario for the time t = 20
min.
Table 1. The positions, courses and speeds of the own ship and
the target ships at the start time (decision time 3 min.)
Speed
[knots]
Course
[degrees]
x [n.m.]
y [n.m.]
15
0
0
0
8
90
4
-0.5
10
0
-6
5
15
79
-6
3
In Figure 2 the arrow indicating the end of the
own speed vector is on the light grey area, which
means a close but relatively safe encounter with
target 3 (no domain violation). In Figure 3.the
situation is still safe but the forbidden region has
enlarged significantly due to the own ship
approaching the target 3. The forbidden region is
continuously increasing which is shown in Figure 4.
In Figure 5 the forbidden region has changed
because the own ship is currently passing target 3.
Once the own ship has passed the target 3, the
forbidden region decreases rapidly, which is
illustrated by Figure 6.
362
4 AN EXEMPLARY SCENARIO OF USING
FCTPA FOR PLANNING THE LAST CHANCE
MANOEUVRE
In this section the situation involving the last chance
manoeuvre is presented. It is assumed here, the start
data for this scenario is the same as for the situation
in section 3, however, after 12 minutes from the
start, when the closest target is about 3 nautical
miles from the own ship it alters its course
unexpectedly in such a way, that the own ship is
forced to perform the last chance manoeuvre.
The input data for this scenario is given in
Figures 7 -8 and in Table 2. Figure 7 depicts the
situation before target 3 altered its course by 41
degrees.
Fig. 7. The FCTPA for the given scenario for the time t = 11
min. (before target 3 has altered its course)
Fig. 8. The FCTPA for the given scenario for the time t = 12
min. (after target 3 has altered its course by 41 degrees)
Table 2 presents the data for the situation after
target 3 has altered its course (t = 12 min.)
Table 2. The positions, courses and speeds of the own ship and
the target ships after target 3 has altered its course (decision
time 3 min.)
Speed
[knots]
Course
[degrees]
x [n.m.]
y [n.m.]
15
0
0
0
8
90
5.6
-0.5
10
0
-6
0
15
58
-3.1
0.6
Figure 8 depicts the situation after target 3 altered
its course by 30 degrees. The end of the arrow
indicating the own speed vector is on the dark grey
area, which means that there is a significant collision
risk (possible domain violation). It might be
concluded from Figure 8, that to avoid the collision,
the own ship should take one of the following
actions within a 3-minute decision time:
− alter its course to the starboard by approximately
75 degrees,
− reduce its speed from 15 to 5 knots,
− alter both its course and speed, for example
reduce the speed from 15 to 8 knots and alter its
course by approximately 60 degrees to the
starboard.
5 SUMMARY
In the paper a visualization method – FCTPA has
been introduced. It is based on the CTPA method
and offers new features: fuzzy sectors of forbidden
speed and course values and the possibility to use
any given ship domain. The method enables the
navigator to assess an encounter situation and plan a
collision avoidance manoeuvre if necessary. It is
especially useful for planning last chance
manoeuvres because the navigator can choose a
combination of course and speed alteration
manoeuvre quickly without performing any
additional computations.
REFERENCES
Coldwell T.G. 1982. Marine Traffic Behaviour in restricted
Waters, The Journal of Navigation vol. 36: pp. 431-444.
Lenart A.S. 1982. Collision threat parameters for a new radar
display and plot technique, The Journal of Navigation vol.
36: pp. 404-410.
Pietrzykowski Z. 2001. Ship Fuzzy Domain on a Straight
Section of a Fairway – Comparative Study, The IX
International Scientific and Technical Conference on
Maritime Traffic Engineering, Szczecin.
Szlapczynski R. 2006. A unified measure of collision risk
derived from the concept of a ship domain, The Journal of
Navigation vol. 59: pp. 477-490.